江苏省南通市2021届高三月考模拟测试(2020.9)附答案
江苏省南通市2021届高三月考模拟测试(2020.9)
1江苏省南通市2021届高三月考模拟测试数学试题2020.9一、单项选择题：本题共8小题，每小题5分，共40分。
在每小题给出的四个选项中，只有一项是符合题目要求的。
1． 03x <<是12x -<成立的（ ） A ．充分不必要条件 B ．必要不充分条件 C ．充要条件D ．既不充分也不必要条件2．12i 12i1i 1i-++=+-（ ） A ．1- B ．i - C ．1 D ．i3．设D 为ABC △的边BC 的延长线上一点，3BC CD =，则（ ） A ．1433AD AB AC =-B ．4133AD AB AC =+ C ．1433AD AB AC =-+D ．4133AD AB AC =- 4． 已知直线1l ：360x y +-=与圆心为()0,1M 5的圆相交于A ，B 两点，另一直线2l ：22330kx y k +--=与圆M 交于C ，D 两点，则四边形ACBD 面积的最大值为（ ） A ．102B ． 52C ．)521D ．)5215． 一个正三棱锥(底面积是正三角形，顶点在底面上的射影为底面三角形的中心)的四个顶点都在半径为1的球面上，球心在三棱锥的底面所在平面上，则该正三棱锥的体积是（ ）1A 33B 3C 3D 3 6． 当动点P 在正方体1111ABCD A B C D -的棱DC 上运动时，异面直线1D P 与1BC 所成角的取值范围（ ） A ．π,6π4⎡⎤⎢⎥⎣⎦B ．π,6π3⎡⎤⎢⎥⎣⎦C ．π,4π3⎡⎤⎢⎥⎣⎦D ．π,3π2⎡⎫⎪⎢⎣⎭7．已知椭圆()2222:10x y E a b a b+=>>的左，右焦点分别为1F ，2F ，过1F 作垂直x 轴的直线交椭圆E 于A ，B 两点，点A 在x 轴上方．若3AB =，2ABF △的内切圆的面积为9π16，则直线2AF 的方程是（ ） A ．3230x y +-= B ．2320x y +-= C ．4340x y +-=D ．3430x y +-=8． 已知()3ln 44x f x x x=-+，()224g x x ax =--+，若对(]10,2x ∀∈，[]21,2x ∃∈，使得()()12f x g x ≥成立，则a 的取值范围是（ ） A ．1,8⎡⎫-+∞⎪⎢⎣⎭B ．258ln 2,16-⎡⎫+∞⎪⎢⎣⎭C ．15,84⎡⎤-⎢⎥⎣⎦D ．5,4⎛⎤-∞ ⎥⎝⎦二、多项选择题：本题共4小题，每小题5分，共20分。
江苏省南通市海安高级中学2020-2021学年高三上学期9月月考数学试题
参考答案
1．
【分析】
利用集合交集的定义可求出集合 .
【详解】
因为集合 ， ，
所以 ，故答案为 .
【详解】
依题意 ，即 ，解得 .
【点睛】
本小题主要考查具体函数定义域的求法，主要是偶次方根的ቤተ መጻሕፍቲ ባይዱ开方数为非负数，考查一元二次不等式的解法，属于基础题.
5．
【分析】
设长方体 的底面积为 ，高为 ，可得出 ，则三棱锥 的底面积为 ，高为 ，再利用锥体的体积公式可计算出三棱锥 的体积.
（Ⅰ）求b，c的值；
（Ⅱ）求sin（B–C）的值．
16．如图，在直三棱柱 中， ，点 为棱 的中点， 与 交于点 ， 与 交于点 ，连结 .
求证：（1） ；
（2）平面 平面 .
17．现有一张半径为 的圆形铁皮，从中裁剪出一块扇形铁皮（如图 阴影部分），并卷成一个深度为 的圆锥筒，如图 .
（1）若所裁剪的扇形铁皮的圆心角为 ，求圆锥筒的容积；
3．
【分析】
根据分层抽样总体和样本中， 型号的产品所占的比例相等列等式求出 的值.
【详解】
由于在总体和样本中， 型号的产品所占的比例相等，则有 ，解得 ，
故答案为 .
【点睛】
本题考查分层抽样中的计算，解题时要根据分层抽样的特点列等式进行计算，考查运算求解能力，属于基础题.
4．
【分析】
根据偶次方根被开方数为非负数列不等式，解不等式求得函数的定义域.
2020-2021学年江苏省南通中学高三英语月考试卷及答案
2020-2021学年江苏省南通中学高三英语月考试卷及答案第一部分阅读（共两节，满分40分）第一节（共15小题；每小题2分，满分30分）阅读下列短文，从每题所给的A、B、C、D四个选项中选出最佳选项AAlex Palmer says he'll never forget his 13th birthday, not because of a gift or a party, but fire. “It made me realize how valuable life is,” said Alex, a seventh grader atMonroeDemonstrationSchoolinTulsa,Oklahoma.On April 18, Alex and many other kids from his school were riding home on a school bus when they suddenly saw smoke coming from the bus’ engine. “It was jaw-dropping,” he told reporters.By the time Alex and some other kids made it out the bus’ back door, the bus was already on fire. And some of their schoolmates were still inside. So he and some of the other older kids took action.“One little kid was slowing everyone down with his big backpack, ” eighth grader Destiny Fain said, “so I got it off and threw it to the side and helped to make sure all the little kids weren’t fighting or pushing. ”As that was going on, sixth grader Marketez Doyle-Smith reportedly helped another classmate who had trouble in breathing because of the smoke. “We saw our friend lying on the ground,” he said, “so we took our shirts off and waved them to get him some air to breathe.”Marketez also reportedly stopped a younger kid trying to get back on the bus to search for something he’d left behind. “We're all a family,” he told reporters. “So I went back to help the little kid.”Finally everyone made it off safely, thanks to Alex, Destiny, Marketez and several other kids. By later that day, they were already being called heroes. “I really don’t see it as being a hero,” Alex said, according to The World. “I see it as the right thing to do—helping others before you help yourself.”1. What happened on Alex’ s way home?A. The school bus was on fire suddenly.B. There was a party for Alex’s birthday.C. He received a gift from his classmate.D. Some classmates quarreled with each other.2. By saying "We're all a family.” Marketez probably meantA. We’re brothers in the same family.B. It’s our duty to help each other.C. We’re classmates in the same class.D. The thing left on the bus is mine.3. According to the last paragraph, Alex thought that heA. was not a brave student.B. had the right to do anything.C. had just done what he should do.D. hated to be called a hero by others.BMy wife and I recently completed a day-long tour of the Great Wall with Jessie. In addition to being very knowledgeable about the history of theareas that we toured, she spoke excellent English and was able to answer all of our questions. Her driver was very experienced and polite, and we really enjoyed being able to have a customized tour that avoided the tourist traps and forced shopping that seem to be a part of the larger group tours.The attractions themselves were fantastic. I was a little worried that the snowy weather might impact our trip to the Great Wall, but everything went fine, and there weren’t many people out at all that day. I suggest wearing strong shoes—the Great Wall is really a hike. And in snowy or rainy days, the surfaces are pretty slippery (滑的)! Seeing this area in winter was really unique, and the snow made for great pictures. Jessie kept us entertained with stories and facts about the construction of the Wall, and always pointed out great spots for taking pictures. Even though she’s in fantastic shape, she cared about our level of fitness and often stopped to let us catch our breath.When we got back to our hotel, Jessie gave us a great recommendation for dinner and some tips for our planned stops the next day. If I find myself in Beijing in the future, I will certainly be contacting Jessie for more tour opportunities, and I’ve already recommended her to some friends who are visiting the area later in the year. I can’t say enough about how kind and knowledgeable she was, and she really gave us a great tour experience.4. What can we infer about Jessie?A. She is a tour advisor.B. She is a tour guide.C. She is a foreign traveler.D. She is a skilled driver.5. When did the writer visit the Great Wall?A. In spring.B. In summer.C. In autumn.D. In winter.6. What did the writer think of his tour?A. Adventurous.B. Disappointing.C. Satisfactory.D. Improvable.7. What is the probable title for the text?A. A Wonderful Tour Day with JessieB. An Extraordinary Tour CompanyC. The Great Wall, an Excellent AttractionD. Jessie, a Kind and Knowledgeable GuideCJeff Bezos, Elon Musk and Richard Branson have a combined net worth of 400 billion, roughly the size of the GDP of the entire nation of Ireland. And all three men have decided to put vast sums of their wealth into chasing their space travel dreams, creating a modern space race in which ultra — rich men — rather than countries — shoot for the stars.But why the three billionaires choose the crazy plan? Just for the travel dreams? It’s not that simple.As we all know, the space travel is a mirror of comprehensive national strength, whether it’s the cold war or the present. The first space racespannedmultiple presidents and premiers — Kennedy, Krushchev, Brezhnev, Nixon. It made heroes of astronauts and cosmonauts, and it focused national prides. But obviously, this year’s race between the billionaires features none of that national pride or opposing ideas. It’s tax — averse tycoons (大亨) who want to sell high — priced tickets to rich people interested in experiencing weightlessness. Amazon’s Bezos has said he is funding his portion by selling off large chunks of his Amazon stock (股票) — 1 billion or more a year.What are the odds? If anyone is taking bets on how this will end, and who will have the more profitable space tourism business, consider Amazon’s method of making very little profit in order to eat up competition. So, from this point of view, what’s hiding behind this crazy race is business. As a method of expand influence, it is not a bad idea.Richard Branson has carried out his plan on July 12, and Jeff Bezos announced that he will start his space travel on July 20. Bezos is getting some good press because he’s taking Wally Funk along for the ride. She’s the pilot now in her 80s who was kept out of space in the 1960s because she’s a woman. This may be a bonus for him. As for Musk, he thinks these two above are not real space trips, he wants a larger move.Who will win the race in the end? Let’s wait and see.8. Which of the following people might be the potential client of the space travel?A. Daisy aged 45 with a heavy debt.B. Clarkson who doesn’t enjoy taking risks.C. Billy aged 60 with an ample retirement pension.D. Alexander who knows nothing about space travel.9. What stopped Wally Funk flying to space in the 1960s?A. Age.B. Gender.C. Height.D. Disposition.10. What does the author think of the billionaires race?A. Profit — driven.B. Meaningless.C. Foolish.D. Generous.11. What does the underlined word “spanned” in paragraph 3 probably mean?A. Revolved.B. Turned down.C. Entered.D. Leapt through.DPeggy Whitson's job demands a daily twohour workout in a gym where weight has no meaning and the view changes at 17,000 miles an hour.Whitson makes it look easy. At 57, she is the oldest woman to fly in space, breaking the record last November, 2016, when she began her third longterm stay at the International Space Station. After returning home in September, 2017, the NASA astronaut feltmatter-of-factabout the age milestone.“It wasn't a record I was seeking for,” Whitson said. “I was 42 and 48 for my first two space flights. I feel lucky that I was able to get to do another one in my 50s. I don't think people should let age discourage them, even on those jobs that require some amount of physical fitness. The oldest man is John Glenn (at 77), and we've had male astronauts in their 60s before, so it's just a matter of time before women start flying in space at this age”.On the earth, she stays fit by weightlifting, biking, playing basketball and water skiing. She shared what it's like to live in microgravity: “It's like you're in a swimming pool, but you don't have to worry about breathing. If I push off from one side, I'm going to float to the other side. Every direction feels exactly the same, which is really hard for your brain to grasp, but it's amazing how fast you adapt.It's a big shock for the body to come back to Earth—everything is so heavy. We spend a lot of time getting used to being back in gravity again. Back pain was really the most dramatic for me this time. For me, coming home is harder than going up into space.”12. How long did Peggy Whitson spend for her third stay in the International Space Station?A. About 300 days.B. About 708 days.C. About 107 days.D. About57 days.13. What does the underlined word probably mean in the passage?A. Amazing.B. Not surprising.C. Enthusiastic.D. Unbelievable.14. According to the passage, which of the following is true?A. Peggy Whitson likes swimming most.B. Peggy Whitson is the oldest person to fly in space.C. Peggy Whitson had been in space in 2002 and 2008.D. There had been female astronauts over 60s flying in space before.15. Which of the following will Peggy Whitson probably say?A. You can still be successful and do physical things when old.B. I spent quite a lot of time getting used to the life in space.C. The moment we reached the earth, we felt so relaxed.D. I feel lucky that I am physically well after the whole journey.第二节（共5小题；每小题2分，满分10分）阅读下面短文，从短文后的选项中选出可以填入空白处的最佳选项。
江苏省南通市海安高级中学2020-2021学年高三生物月考试卷含解析
江苏省南通市海安高级中学2020-2021学年高三生物月考试卷含解析一、选择题（本题共40小题，每小题1.5分。
在每小题给出的四个选项中，只有一项是符合题目要求的。
）1. 如图表示细胞膜的亚显微结构，其中a和b为两种物质运输方式，下列对细胞膜结构和功能的叙述中错误的是（）A. 如图示小肠上皮细胞膜，则CO2的跨膜运输方式是bB. 适当提高温度将加快②和③的运动速度C. 细胞间的识别、免疫、细胞的癌变与②有密切的关系D. a过程需要载体蛋白，该过程充分体现了细胞膜的选择透过性参考答案：C【详解】试题分析：如图示小肠上皮细胞膜，则CO2的跨膜运输方式是自由扩散，b表示的是自由扩散，所以A正确；适当提高温度将加快细胞膜的流动性，会加快②和③的运动速度，所以B正确；细胞间的识别、免疫、与②有密切的关系，但是癌变是原癌基因和抑癌基因突变导致的，所以C错误；a过程需要载体蛋白，该过程充分体现了细胞膜的选择透过性，所以D正确。
2. 用某种酶进行有关实验的结果如下图所示，下列有关说法错误的是A. 由图1实验结果可知该酶的最适催化温度为30℃左右B. 图2和图4能说明该酶一定不是胃蛋白酶C. 由图4实验结果可知酶具有高效性D. 由实验结果可知酶具有专一性参考答案：C【分析】酶是活细胞产生的具有催化作用的有机物，绝大多数是蛋白质，少数是RNA。
酶的特性：专一性、高效性、作用条件较温和。
影响酶活性的因素：温度、pH等，在最适温度（pH）下，酶的活性最高；当温度（pH）低于最适温度（pH）时，酶的活性随温度（pH）的升高而增强；当温度（pH）高于最适温度（pH）时，酶的活性随温度（pH）的升高而减弱。
分析题干和题图可知本题是影响酶活性的因素，先解读曲线，然后根据选项描述分析判断。
【详解】A、分析题图1说明在这三个温度中，30℃比较适宜，该酶的最适催化温度为30℃左右，A 正确；B、分析题图2曲线可知，酶的最适pH为7，而胃蛋白酶的最适宜pH是2左右，由图4可知，该酶能分解麦芽糖，应该是麦芽糖酶，所以该酶一定不是胃蛋白酶，B正确；CD、由图4知，该酶能分解麦芽糖，不能分解蔗糖，说明酶具有专一性，C错误，D正确。
2020-2021学年江苏省南通中学高三语文三模试题及参考答案
2020-2021学年江苏省南通中学高三语文三模试题及参考答案一、现代文阅读（36分）(一)现代文阅读I(9分)阅读下面的文字，完成各题。
秋思白先勇华夫人将她那只左手伸了出去，觑起眼睛，自己观赏着，她左手的指甲已经修剔过了，尖尖的，晶莹闪亮，一把春葱似的雪白手指，玲珑地翘了起来，食指上套着一枚绿汪汪的翡翠环子。
“夫人，”女佣阿莲走进来报告道，“万大使夫人又打电话来催。
秦夫人、薛夫人都到了，请夫人马上到万公馆去。
”“这几个麻将精！”华夫人摇头笑叹道，款款地立起身，“天天都来捉我，真教她们缠的受不了。
”华夫人走到花园里，一阵凉风迎面吹过来，把她的大衣都撩开了。
她赶忙将大衣扣子扣上，一面戴上她那副珠灰的丝手套。
园子里一道夕阳，斜铺在草坪上，那些朝鲜草草尖子已经泛着点点的黄斑，通到大门的那条石径上，几片落叶，给风吹得簌簌地在打转子。
华夫人在石径上走了几步，突然一阵冷香，袭到了她面上来，她回头望去，看见墙东一角，那一片“一捧雪”开得翻腾了起来，她不由得停下脚步，若有所思的迟疑了片刻，终于回头踅了过去。
她踱到那畦“一捧雪”眼前，俯下身，深深吸了一口气。
①那几十株齐腰的白菊花，一团团，一簇簇，都吐出拳头大的水晶球子来了，白茸茸的一片，真好像刚落下来的雪花一般，华夫人又凑近一朵大白菊，嗅了一下。
人家都说这就是台湾最上品的白菊花了，在新公园的花展还得过特别奖呢，只是太娇弱了些，去年种下去，差不多都枯死了，她叫花匠敷了一个春天的鸡毛灰，才活过来，倒没料到，一下子，竟开得这般繁盛起来了。
怪道上次万吕如珠来的时候，这些“一捧雪”刚打苞，她已经抱怨她：华夫人，你这些菊花真的那么尊贵吗？也舍不得送我们两枝插插盆。
华夫人掐下一枝并蒂的菊花，一对花苞子颤袅袅的迎风抖着，可是她知道万吕如珠最是个好虚面子，嘴上不饶人的女人，花苞子选小些给她，恐怕都要遭她哂笑一番呢。
华夫人跨进了那片花丛中，巡视了一番，她看到中央有一两棵花朵特别繁盛，她走向前去，用手把一些枝叶拨开，在那一片繁花覆盖着的下面，她赫然看见，②原来许多花苞子，已经腐烂死去，有的枯黑，上面发了白霉，吊在枝丫上，像是一只只烂馒头，有的刚委顿下来，花瓣都生了黄锈一般，一些烂苞子上，斑斑点点，爬满了菊虎，在啃啮着花心，黄浊的浆汁，不断的从花心流淌出来。
江苏省南通中学2021届高三下期模拟试题(新高考)
江苏省南通中学2020-2021学年高三下期模拟试题（新高考）英语试题注意事项：1.本试卷由四个部分组成。
其中，第一、二部分和第三部分的第一节为选择题。
第三部分的第二节和第四部分为非选择题。
2.答卷前，考生务必将自己的姓名、准考证号填写在答题卡上。
3.回答选择题时，选出每小题答案后，用2B铅笔把答题卡上对应题目的答案标号涂黑;回答非选择题时，将答案写在答题卡上,写在本试卷上无效。
4.考试结束后，将本试卷和答题卡一并交回。
第一部分阅读理解(共两节,满分50分)第一节(共15小题；每小题2.5分, 满分37.5分)阅读下列短文, 从每题所给的A、B、C和D四个选项中, 选出最佳选项。
AIt's always adventurous and romantic to visit an island country. Take a look at some breathtakingly beautiful island countries in the world, which everyone should visit at least once in his lifetime.MaldivesIt's believed that Maldives is one of the most popular honeymoon places as well as one of the most beautiful island countries. Situated in the middle of the Indian Ocean, Maldives is made up of a series of ancient coral reefs that grow up along the sides of ancient volcanoes, with fascinating beaches.FijiFiji has plenty of surprises for any adventurous travelers. It is famous for the world's best surf scenes, attracting many surfing lovers to ride the great waves. Well, if surfing is not for you and you love sitting on the beach and relaxing, hiking or seeing breathtaking waterfalls, Fiji is also a suitable island country to visit.MaltaMalta, a beautiful southern European country in the Mediterranean Sea, has a rich history and culture. There are amazing sky-high cliffs to climb, wonderful temples to visit and lots of amazing places to go diving. There are plenty of interesting things to explore here and everyone can find something to enjoy. The historic part of Malta is shown in its architecture, great walled cities, and many underground tunnels.1．Which place will be most likely to be chosen by a newly-married couple according to the text?A．The Mediterranean Sea. B．Maldives.C．Malta. D．Fiji.2．What is the special part about Fiji?A．You can see the world’s most breathtaking waterfalls.B．It is surfing lovers' favourite island country.C．There are sky-high cliffs to explore.D．You can try the world's longest tunnels.3．What can tourists do in Malta?A．Hike on green plains. B．Ride the greatest waves.C．See breathtaking waterfalls. D．Explore underground tunnels.BWe moved into a beautiful two-story old house.The house was built in 1956. It was repaired in 2003.At first, really small things began to happen. They didn’t make me believe that something was wrong, but as time went on, things started becoming stranger and stranger. Early something was missing, and later on it would be found somewhere else. I just thought I had forgotten where I put it, or perhaps my daughter was playing around with things. Then later on I would hear strange sounds when nobody was at home but me. Yet it was an old house, and sometimes old houses did make little noises, so again, I didn’t really mind.Then things that I couldn’t explain started happening. It was last November and I was at home alone cleaning the house. When I was sweeping the kitchen floor, I felt a very cold wind blowing my hair. I thought the kitchen window must have been opened, but when I checked it, it was closed. The windows were new, and there was no way any cold air came in.We all felt very strange and moved away from there in October, 2014. I was never really frightened. It was just strange, like something or someone was trying to get my attention or something.4．The house is ________years old.A．about 97 B．over 100C．over 200 D．about 645．According to the passage, the things that were missing in the old house ________.A．would never be foundB．can’t be explained by the writerC．would be seen in another placeD．were put somewhere else by the writer6．At first the writer didn’t mind the strange sounds happened because ________.A．the house was very old B．someone made themC．her daughter made them D．the cold wind was blowing7．The writer’s attitude (态度) to the old house is ________.A．strange B．frightenedC．surprised D．lovingCWhile traditional wisdom tells us that we should eagerly catch every opportunity that comes our way, playing a little hard to get has its advantages. Studies have shown that opportunities are seen to be more valuable as they become less available, according to Robert Cialdini, a leading expert on influence, who said “What the scarcity principle says is that people are more attracted to rare opportunities.”Appearing available can work against you, according to Jeremy Nicholson, a social psychologist. If you're excited about a work opportunity, it indicates that you are in low demand.“Making something harder to get,” Dr. Nicholson said, “tends to increase at least the perception of value.” If you are meeting with hiring managers or potential clients, Dr. Nicholson recommends that responding in a way that respects their interest without being too eager. Dr. Nicholson advises, with respo nses like: “I do have a couple of other projects to deal with. However, I could do this for you if you want.”“It's easy to become excited when an opportunity presents itself,” Ms. Ryan, founder of Human Workplace, said, “but remember that your power in an y negotiation is related to your ability to walk away. Don't accept an offer before fully considering the opportunity.” Once you have interest, turn that into diligence. Ms. Ryan recommends reading up on the organization from third-party perspectives, and checking out job-search websites to see what employees and ex-employees say about it. Keep in mind: The goal is to approach any negotiation cautiously and with a clear head.Appearing less available isn't about limiting our enthusiasm, but about trusting in our own self-worth so we can be proactive, experts say. This means mindfully transforming our excitement into strategy. “Emphasizing the uniqueness of your resources and your cooperative approach can help you more quickly advance your goals,” said Shirli Kopelman, a professor at the Ross School of Business at the University of Michigan.8．Why is it necessary for us to appear scarce when we face opportunities?A．Because we should strictly follow the principle about scarcity.B．Because we should eagerly grasp opportunities coming our way.C．Because we should value opportunities in the competitive society.D．Because we should show rare opportunities to increase our advantages.9．What does the underlined word “proactive” mean?A．Accessible. B．Strategic. C．Enthusiastic. D．Limited.10．Which of the following statements is the suggestion given by Ms. Ryan?A．Being eager enough and ready. B．Being cautious and clear headed.C．Being confident and interested. D．Being skillful and accomplished.11．According to Shirli Kopelman, which is the best way to help us achieve our goals?A．Not being too hard on our career. B．Noting controlling our enthusiasm.C．Applying excitement to negotiations. D．Stressing scarcity and cooperation ways.DGrowing up, we are constantly reminded that young people are heavily affected by technology. We are the “antisocial club”, those who prefer to text our friends in the same room rather than make eye contact with them. And even though never-ending studies reveal to us the extent of our social media addiction, we should at least consider that it’s not only our young people’s problem any more.There’s the rise of the Instagram mums, who like to post an abundance of cute baby pictures, share their mom feelings along the way and show their wonderful lifestyles. They are the so-called “Facebook mum generation”, a growing group of parents that like to overshare.While all of this might be fine, and even a little humorous, new research suggests that parents’ technology addiction is negatively a ffecting their children’s behavior. According to the study, 40% of mothers and 32% of fathers have admitted having some sort of phone addiction. This has led to a significant fall in verbal interactions within families and even a decline in mothers’ encour aging their children.There is no denying that I get annoyed when receiving the words “I’ll be with you soon” from a parent, when all I want to do is ask one question. But, at the same time, every day leaving the room to wait until my father is finished wi th his “serious business” (Farmville), has now become the norm. Whether you want to escape your disturbing children for a bit, or want to stay up late flicking through Twitter, know that wanting to do all of these is normal. We, your children, know how addictive it can be and how difficult it is to switch off. But before telling us to put our phones away at the table or even worse, listing statistics of how damaging social media can be for us, maybe lead by example, considering how much time you spend on the phone and how thisis impacting your children and your relationship with us. Maybe in this way we can work on our addiction together.12．From Paragraph 1, we can know that teenagers nowadays ________.A．enjoy socializing with their friends B．send messages to their friends every dayC．hate to make eye contact with their friends D．are heavily addicted to their mobile phones13．What does the author think of mums’ oversharing?A．Boring. B．Selfish. C．Funny. D．Meaningful.14．The underlined word “norm” in Paragraph 4 probably means ________.A．security B．standard C．routine D．custom15．What’s the main purpose of the article?A．To share the author’s own experience with the readers.B．To call on parents to get rid of their own media addiction.C．To reveal that parents are always addicted to mobile phones.D．To show the author’s dissatisfaction with parents’ phone use.第二节(共5小题；每小题2.5分, 满分12.5分)A new urban sport, parkour, is hitting the streets. It has evolved from obstacle course training into a fitness option for young people. In parkour, the outside world is the gym! 16． The goal of parkour is a direct route from one place to another. You meet an obstacle, you overcome it.Mark Toorock, who teaches the techniques of parkour at his fitness gym, says that parkour is a method to train the body and mind using obstacles as the medium. He says that this new sport is demanding and takes years to master. 17．But Toorock, who used to be a martial arts expert, says that everyone can benefit from learning the basic skills involved in parkour like running, jumping and crawling (爬行). These are the things that humans used to have to do all the time. 18． The original idea of parkour was to return to running and jumping as basic elements in moving from one place to another.Georges Hebert, a French navy officer, was so impressed by the effortless athleticism of African tribes that he devised a training method based on running, climbing, jumping, balancing and throwing. The word parkour comes from parcours de combatant, the French term for a military obstacle course. 19．Dr Kenneth Kao explains that the sport of parkour is not extreme — it is the environment which is extremeand dangerous. Being outside, jumping off railings and flipping over park benches can be quite frightening, so parkour courses in gyms concentrate on practicing all the individual moves to make everything easier. 20．However, that is not real parkour because it’s indoors with a fixed obstacle. The goal for everyone is to go outdoors.A．Gyms provide thick floor matting (垫子) for rolling and rubberized boxes for jumping over.B．The bridges, buildings and railings (栏杆) of each and every city are the equipment.C．Every action in parkour is natural, so everyone must have the ability to move in this way.D．Parkour was introduced into china in recent years and has gained popularity.E.But today, due to modern transport, these basic skills are no longer used on a regular basis.F.The French word for people who participate in the sport is traceurs or traceuses.G.Beginn ers should realize that they won’t be jumping over buildings any time soon!第二部分语言运用(共两节, 满分30分)第一节(共15小题；每小题1分, 满分15分)The little boy with big brown eyes was waiting for us on the other side of the world. Ever since our adoption agency had 21 us, I’d been hurriedly competing all the necessary paperwork. I made it a personal goal to never delay the process. On one late afternoon in June. I rushed toward the closest FedEx office. I had some 22 to send overnight, and I wanted them to go out that day.I thought I knew where the FedEx office was. I drove there as the minutes slipped away, only to find that the office was no longer 23 where I remembered it. Tears came to my eyes. This was 24 we all had a smartphone in our pockets. I had no way of 25 the correct location. 26 , I started driving toward home. I felt like a failure, as though I’d just 27 my new son to more days in an orphanage waiting for us.Suddenly, I was 28 at a stoplight by an oversized box truck My anger turned to 29 when I saw the sign. It was a FedEx truck I 30 closely behind the truck. What were the 31 the truck would lead me straight to the FedEx office I was seeking?It broke out the chances were good. Less than five minutes later, I saw a FedEx sign, and the truck made a turn into the parking lot. I had 32 in my eyes again.Our documents went out that night. The truck driver 33 knew he was an angel for me that day. Three months later, we flew halfway around the world to 34 our son for the first time. We have been with him every day since.Miracles are always around us 35 we are open to them. Sometimes, it’s a smile at the right time or a kindword. And ever y now and then, it’s even a big truck that cuts us off in traffic.21．A．debated B．challenged C．matched D．scanned22．A．gifts B．letters C．documents D．postcards23．A．locked B．located C．ranked D．repaired24．A．before B．after C．since D．when25．A．finding B．choosing C．describing D．showing26．A．Bored B．Delighted C．Disappointed D．Surprised27．A．compared B．sentenced C．appointed D．accompanied28．A．kept up B．put down C．taken in D．cut off29．A．guilt B．panic C．shock D．terror30．A．ran B．arose C．walked D．followed31．A．chances B．wonders C．doubts D．promises32．A．dust B．dirt C．tears D．sands33．A．just B．never C．exactly D．immediately34．A．free B．meet C．beat D．spoil35．A．if B．although C．unless D．until第二节(共10小题；每小题1.5分, 满分15分)阅读下面短文, 在空白处填入1个适当的单词或括号内单词的正确形式。
江苏省南通市启秀中学2020-2021学年高三数学理模拟试题含解析
江苏省南通市启秀中学2020-2021学年高三数学理模拟试题含解析一、选择题：本大题共10小题，每小题5分，共50分。
在每小题给出的四个选项中，只有是一个符合题目要求的1. 已知O是坐标原点，点，若点为平面区域上的一个动点，则的最大值是（）A．-1 B． C．0 D．1参考答案：D略2. 复数（为虚数单位）在复平面内对应点的坐标是（）A． B． C． D．参考答案：A，复数（为虚数单位）在复平面内对应点的坐标是故选A．考点：复数的运算及几何意义．3. 函数f（x）=sin（2x+φ）（|φ|＜π）的图象向左平移个单位后关于原点对称，则函数f（x）在[0，]上的最小值为（）A．﹣B．﹣C．D．参考答案：A【考点】函数y=Asin（ωx+φ）的图象变换．【专题】三角函数的图像与性质．【分析】由函数图象的平移得到，再由函数为奇函数及φ的范围得到，求出φ的值，则函数解析式可求，再由x的范围求得函数f（x）在[0，]上的最小值．【解答】解：函数f（x）=sin（2x+φ）图象向左平移个单位得，由于函数图象关于原点对称，∴函数为奇函数，又|φ|＜π，∴，得，∴，由于，∴0≤2x≤π，∴，当，即x=0时，．故选：A．【点评】本题考查了函数y=Asin（ωx+φ）型函数的图象和性质，考查了三角函数值域的求法，是中档题．4. 曲线（θ为参数）的对称中心（）A．在直线y=2x上B．在直线y=﹣2x上C．在直线y=x﹣1上D．在直线y=x+1上参考答案：B【考点】圆的参数方程．【专题】选作题；坐标系和参数方程．【分析】曲线（θ为参数）表示圆，对称中心为圆心，可得结论．【解答】解：曲线（θ为参数）表示圆，圆心为（﹣1，2），在直线y=﹣2x上，故选：B．【点评】本题考查圆的参数方程，考查圆的对称性，属于基础题．5. 已知是上最小正周期为2的周期函数，且当时,,则函数的图象在区间[0,6]上与轴的交点的个数为（）（A）6 （B）7 （C）8 （D）9参考答案：B6. 执行右边的程序框图。
2020-2021学年江苏省南通中学高三生物月考试卷及答案解析
2020-2021学年江苏省南通中学高三生物月考试卷及答案解析一、选择题：本题共15小题，每小题2分，共30分。
每小题只有一个选项符合题目要求。
1.下图1是种群增长速率随时间变化的曲线，图2是种群数量特征的概念模型，相关分析正确的是A. 根据图1可知，若t0时种群的数量为N，则t2时其为2NB. 根据图1可知，t1→t2时间内，该种群数量呈上升趋势C. 根据图2可知，春节前后，深圳的人口数量变化主要取决于①、②D. 根据图2可知，③和④依次代表年龄组成、性别比例2.动态突变是指基因中的3个相邻核苷酸重复序列的拷贝数发生倍增而产生的变异，这类变异会导致人类的多种疾病，且重复拷贝数越多，病情越严重。
下列关于动态突变的推断正确的是A. 可借助光学显微镜进行观察B. 只发生在生长发育的特定时期C. 会导致染色体上基因的数量有所增加D. 突变基因的翻译产物中某个氨基酸重复出现3.下列有关水和无机盐的叙述，错误的是（）A.沙漠植物细胞内的水分主要以自由水的形式存在B.在细胞代谢过程中，核糖体、叶绿体、线粒体都能产生水C.玉米种子在萌发时和玉米植株在生长发育阶段吸收水分的方式均为被动运输D.人体体液中的无机盐大多数以离子的形式存在4.接种乙肝疫苗后一般需要间隔1个月、6个月再次注射第二针和第三针，连续接种的主要目的是A. 疫苗被浆细胞特异性识别，产生大量的抗体B. 疫苗刺激T细胞产生大量淋巴因子C. 二次免疫刺激机体产生大量淋巴细胞和抗体D. 增强体液中的吞噬细胞、溶菌酶对病原体的杀伤力5.现有氨基酸810个，其中氨基总数为820个，羧基总数为818个，则由这些氨基酸合成的含有3条肽链的蛋白质共有肽键、氨基和羧基的数目依次分别为A. 798、2和2B. 807、12和10C. 799、1和1D. 807、13和116.下列关于致癌因子的种类及恶性肿瘤预防方法的叙述，错误的是（）A.紫外线、X射线属于物理致癌因子B.烟草中的尼古丁、焦油属于化学致癌因子C.癌症的发生与人的心理状态完全无关D.远离致癌因子是预防癌症的有效手段7.为了验证土壤中的微生物可以将淀粉分解产生还原糖，某研究小组取两只烧杯甲和乙，都放入等量的淀粉溶液20mL，甲中加入30mL制备好的土壤浸出液，乙中放入等量的蒸馏水，在适宜的温度下放置7天(所有操作符合无菌操作要求)。
2020-2021学年江苏南通高三下英语月考试卷
一、单选题
1. To make members of a team perform better, the trainer first of all has to know their ______ and weaknesses.
A.strengthsB.benefitsC.techniquesD.values
18.
M: I have an extra ticket to the concert tonight. Would you like to join me?
W: Thanks, but I already have one. You can ask Emily. She might be interested.
W: We'll need you to join the gym, and then you can find out which classes fit your schedule the best.
What does Jack want to do?
A.Change his work schedule.B.Buy a pair of gym shoes.
A.that; whereB.when; whereC.which; thatD.when; that
8. She says things like this ________ we get together.
A.at every timeB.every time
C.every time whenD.each time that
Here is a piece of news for bird lovers. Scientists have painted a long road, red, yellow and white.
江苏省南通市西城中学2020-2021学年高三英语月考试题含解析
江苏省南通市西城中学2020-2021学年高三英语月考试题含解析一、选择题1. All the things must be done well.A．worth to doB．worthy of being doneC．worthy doingD．worth of doing参考答案：B2. Mother bought many tomatoes from the market two days ago, ________ some have gone bad due to the bad weather.A. of thoseB. from whichC. of whichD. in which参考答案：C3. The other group of Qing Tombs called Xiling _______ about 100 kilometers to the west of Beijing.A. locatesB. sitsC. establishesD. situates参考答案：B4. He did not regret saying what he did but felt that he ____________ it differently.A. could expressB. would expressC. could have expressedD. would have expressed参考答案：C5. After a long absence, I went back to college, ______ to pick up where I'd left off． A．hoping B．hope C．to hope D．hoped参考答案：A略6. There are about 2000 students in our school , many of ______ come from the countryside.A.themB. whomC. thoseD. who参考答案：B7. Naturally, when the important festival comes in China, banger(鞭炮) ___and everyone feels happy. A. take off B. go off C. switch off D. turn off参考答案：B略8. — May I stop here?— No, you ___________.A. mustn’tB. might notC. needn’tD. won’t参考答案：A试题分析：考查情态动词。
2021年江苏省南通中学高三生物月考试卷及参考答案
2021年江苏省南通中学高三生物月考试卷及参考答案一、选择题：本题共15小题，每小题2分，共30分。
每小题只有一个选项符合题目要求。
1.某人因交通事故导致表达性失语症，即患者可以看懂文字、听懂别人谈话，但自己却不会讲话，不能用词语表达意思，他很有可能使大脑皮层的哪个语言区受伤？（）A.H区B.S区C.V区D.W区2.下图是人体某组织结构示意图，①②③④分别表示人体内不同部位的液体。
据图判断下列说法正确的是（）A. 人体的内环境是由①②③组成的B. ②中含激素、血红蛋白、乳酸、CO2等物质C. 某人长期营养不良，则会引起③液和①液的减少D. ③液和①液的成分相同3.下列关于生态系统自我调节能力的叙述中，错误的是（）A.森林中，害虫数量增加时，食虫鸟也会增多，害虫种群的增长就会受到抑制，这属于生物群落内的负反馈调节B.负反馈调节在生态系统中普遍存在，它是生态系统自我调节能力的基础C.自我调节能力强的生态系统，其稳定性也高D.当外界干扰强度超过一定限度时，生态系统的自我调节能力将会丧失4.如图为人体神经元细胞模式图，据图分析。
下列叙述错误的是（）A.A点属于神经元的轴突部分B. 若控制该细胞的呼吸作用，将影响神经兴奋的传导C. ④中的物质属于神经递质，释放到⑤的方式是胞吞D. 若刺激A点，图中电流计B将发生2次方向相反的偏转5.“制作DNA双螺旋结构模型”的实验中，若有4种碱基塑料片共20个，其中4个C,6个G，3个A，7个T,脱氧核糖和磷酸之间的连接物14个，脱氧核糖塑料片40个，磷酸塑料片100个，代表氢键的连接物若干，脱氧核糖和碱基之间的连接物若干，则A. 能搭建出20个脱氧核苷酸B. 搭建的分子片段中每个脱氧核糖都与2个磷酸相连C. 能搭建出47种不同的DNA分子模型D. 能搭建出一个4碱基对的DNA分子片段6.过敏反应发生机制如图所示。
过敏原可激发体液免疫产生IgE抗体，当过敏原再次入侵机体时，肥大细胞可产生组织胺，使血管壁通透性增加，引起过敏症状。
江苏省南通市实验中学2020-2021学年高三物理月考试卷带解析
江苏省南通市实验中学2020-2021学年高三物理月考试卷含解析一、选择题：本题共5小题，每小题3分，共计15分．每小题只有一个选项符合题意1. 如图所示，半径为R的半圆柱形玻璃砖某一截面的圆心为O点。
有两条光线垂直于水平柱面射入玻璃砖中，其中一条光线通过圆心O，另一条光线通过A点，且。
这两条光线射出玻璃砖后相交于一点，该点到O点距离为R，则玻璃砖的折射率为（）A． B． C． D．2参考答案：C2. （单选）某电站采用6000V的电压进行远距离输电，输送总功率为500kW，测得安装在输电线路起点和终点的电能表一昼夜读数相差4800kWh，下列说法正确的是（）A. 输送电流为12AB. 用户得到的功率为400KwC. 输电效率为60%D. 输电导线的电阻为86.4Ω参考答案：解：A、输送电流为：A．故A错误；B、安装在输电线路起点和终点的电能表一昼夜读数相差4800kWh，则损耗的功率：kW用户得到的功率是：500kW﹣200kW=300kW．故B错误；C、输电效率为：η=100%=60%．故C正确；D、由P=I2R的变形公式得：Ω．故D错误．故选：C3. 空间存在着平行于x轴方向的静电场，其电势ϕ随x的分布如图所示，A、M、O、N、B为x轴上的点，|OA|＜|OB|，|OM|=|ON|。
一个带电粒子在电场中仅在电场力作用下从M点由静止开始沿x轴向右运动，则下列判断中正确的是A．粒子一定带正电B．粒子从M向O运动过程中所受电场力均匀增大C．粒子一定能通过N点D．粒子从M向O运动过程电势能逐渐增加参考答案：C由电势ϕ随x的分布图可知电势随x均匀变化，则可知电场为匀强电场，且O点左侧的电场强度大于右侧的电场强度，左侧场强方向沿x轴负向，右侧场强方向沿x轴正向，由于带电粒子在电场中仅在电场力作用下从M点由静止开始沿x轴向右运动，故粒子一定带负电，粒子从M向O运动过程中所受电场力不变，电场力做正功，电势能减小，粒子从O向N运动过程中所受电场力做负功，做减速运动，由于|OA|＜|OB|，|OM|=|ON|，故粒子一定能通过N点，故只有选项C正确。
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江苏省南通市2021届高三月考模拟测试数学试题2020.9一、单项选择题：本题共8小题，每小题5分，共40分。
在每小题给出的四个选项中，只有一项是符合题目要求的。
1． 03x <<是12x -<成立的（ ） A ．充分不必要条件 B ．必要不充分条件 C ．充要条件D ．既不充分也不必要条件2．12i 12i1i 1i-++=+-（ ） A ．1- B ．i - C ．1 D ．i3．设D 为ABC △的边BC 的延长线上一点，3BC CD =，则（ ） A ．1433AD AB AC =-B ．4133AD AB AC =+ C ．1433AD AB AC =-+D ．4133AD AB AC =-4． 已知直线1l ：360x y +-=与圆心为()0,1M 的圆相交于A ，B 两点，另一直线2l ：22330kx y k +--=与圆M 交于C ，D 两点，则四边形ACBD 面积的最大值为（ ）A ．B ．C ．)51D ．)515． 一个正三棱锥(底面积是正三角形，顶点在底面上的射影为底面三角形的中心)的四个顶点都在半径为1的球面上，球心在三棱锥的底面所在平面上，则该正三棱锥的体积是（ ）A B C D 6． 当动点P 在正方体1111ABCD A B C D -的棱DC 上运动时，异面直线1D P 与1BC 所成角的取值范围（ ） A ．π,6π4⎡⎤⎢⎥⎣⎦B ．π,6π3⎡⎤⎢⎥⎣⎦C ．π,4π3⎡⎤⎢⎥⎣⎦D ．π,3π2⎡⎫⎪⎢⎣⎭7．已知椭圆()2222:10x y E a b a b+=>>的左，右焦点分别为1F ，2F ，过1F 作垂直x 轴的直线交椭圆E 于A ，B 两点，点A 在x 轴上方．若3AB =，2ABF △的内切圆的面积为9π16，则直线2AF 的方程是（ ） A ．3230x y +-= B ．2320x y +-= C ．4340x y +-=D ．3430x y +-=8． 已知()3ln 44x f x x x=-+，()224g x x ax =--+，若对(]10,2x ∀∈，[]21,2x ∃∈，使得()()12f x g x ≥成立，则a 的取值范围是（ ） A ．1,8⎡⎫-+∞⎪⎢⎣⎭B ．258ln 2,16-⎡⎫+∞⎪⎢⎣⎭C ．15,84⎡⎤-⎢⎥⎣⎦D ．5,4⎛⎤-∞ ⎥⎝⎦二、多项选择题：本题共4小题，每小题5分，共20分。
在每小题给出的选项中，有多项符合题目要求。
全部选对的得5分，部分选对的得3分，有选错的得0分。
9．函数()f x 的定义域为R ，且(1)f x +与(2)f x +都为奇函数，则（）A. ()f x 为奇函数B. ()f x 为周期函数C.(3)f x +为奇函数D.(4)f x +为偶函数10．设{})(*N n a n ∈是等差数列，d 是其公差，n S 是其前n 项和.若,,87665S S S S S >=<则下列结论正确的是0.<d A 0.7=a B 59.S S C > 的最大值均为与n S S S D 76.11． 已知双曲线C 过点且渐近线为3y x =±，则下列结论正确的是（）A.C 的方程为2213x y -= B.CC.曲线21x y e -=-经过C 的一个焦点D.直线10x =与C 有两个公共点 12．声音是由物体震动产生的波，期中包含着正弦函数.纯音的数学模型是函数sin y A t ω=，我们听到的声音是由纯音合成的，称之为复合音.若一个复合音的数学模型是函数1()sin sin 22f x x x =+，则下列结论正确的是（）A.2π是()f x 的一个周期 B ．()f x 在[]0,2π上有3个零点C.()f x．()f x 在0,2π⎡⎤⎢⎥⎣⎦上是增函数三、填空题：本题共4小题，每小题5分，共20分。
请把答案直接填写在答题卡相应．．．．．位置上．．．。
13．若6把椅子摆成一排，3人随机就座，则有且仅有两人相邻的坐法有 种(用数字填空)14．在52x ⎛- ⎝的展开式中，2x 的系数为______．15． △ABC 的内角A ,B ,C的对边分别为222,,.=a b c a b c +-∆且，ABC 的面积为S ,36cos cos a S B C =+，则的最大值为__________.16．已知，若方程有2个不同的实根，则实数m 的取值范围是________.(结果用区间表示)四、解答题：本题共6小题，共70分。
请在答题卡指定区域．．．．．．．内作答。
解答时应写出文字说明、证明过程或演算步骤。
17．(本小题满分10分)在ABC △中，3sin 2sin A B =，tan C = （1）求cos2C ；（2）若1AC BC -=，求ABC △的周长．18．(本小题满分12分)已知正项等比数列{}n a 满足3112S S -=，212314a S +=. （1）求数列{}n a 的通项公式； （2）记2212211log log n a n b a a +-=，求数列{}n b 的前n 项和n T .()()ln ,024,24x x e f x f e x e x e <≤⎧⎪=⎨-<<⎪⎩()0f x mx -=19．(本小题满分12分)某机器生产商，对一次性购买两台机器的客户推出两种超过质保期后两年内的延保维修方案：方案一：交纳延保金6000元，在延保的两年内可免费维修2次，超过2次每次收取维修费1500元；方案二：交纳延保金7740元，在延保的两年内可免费维修4次，超过4次每次收取维修费a 元．某工厂准备一次性购买两台这种机器，现需决策在购买机器时应购买哪种延保方案，为此搜集并整理了100台这种机器超过质保期后延保两年内维修的次数，统计得下表：以上100台机器维修次数的频率代替一台机器维修次数发生的概率，记X表示这两台机器超过质保期后延保两年内共需维修的次数．（1）求X的分布列；（2）以所需延保金与维修费用之和的期望值为决策依据，该工厂选择哪种延保方案更合算？20．(本小题满分12分)如图所示，在四面体ABCD中，AD AB⊥，平面ABD⊥平面ABC，AB BC AC==，且4+=．AD BC（1）证明：BC⊥平面ABD；（2）设E为棱AC的中点，当四面体ABCD的体积取得最大值时，求二面角C BD E--的余弦值．21．(本小题满分12分)已知椭圆()2222:10x y O a b a b+=>>的左、右顶点分别为A ，B ，点P 在椭圆O 上运动，若PAB △面积的最大值为O 的离心率为12．（1）求椭圆O 的标准方程；（2）过B 点作圆E ：()2222x y r +-=，()02r <<的两条切线，分别与椭圆O 交于两点C ，D (异于点B )，当r 变化时，直线CD 是否恒过某定点?若是，求出该定点坐标，若不是，请说明理由．22．(本小题满分12分) 已知函数()2113ln 244f x x a x x=+++-，()ln g x x =． （1）求证：()21114f x a x ⎛⎫≥-+ ⎪⎝⎭；（2）用{}max ,p q 表示p q ，中的最大值，记()()(){}max ,h x f x g x =，讨论函数()h x 零点的个数．江苏省南通市2021届高三月考模拟测试数学参考答案一、单项选择题：本题共8小题，每小题5分，共40分。
在每小题给出的四个选项中，只有一项是符合题目要求的。
1. A2. A3. C4.B5.C6. C7. D8. A二、多项选择题：本题共4小题，每小题5分，共20分。
在每小题给出的选项中，有多项符合题目要求。
全部选对的得5分，部分选对的得3分，有选错的得0分。
9.ABC 10. ABD 11.AC 12.ABC三、填空题：本题共4小题，每小题5分，共20分。
请把答案直接填写在答题卡相应．．．．．位置上．．．。
13．72 14．80 15．6 16．1(,)e-∞四、解答题：本题共6小题，共70分。
请在答题卡指定区域．．．．．．．内作答。
解答时应写出文字说明、证明过程或演算步骤。
17．（1）∵tan C 1cos 6C =，∴2117cos 221618C ⎛⎫=⨯-=- ⎪⎝⎭．（2）设ABC △的内角A ，B ，C 的对边分别为a ，b ，c ．∵3sin 2sin A B =，∴32a b =，∵1AC BC b a -=-=，∴2a =，3b =．由余弦定理可得2222cos 13211c a b ab C =+-=-=，则c ABC △的周长为5+18．（1）设数列{}n a 的公比为q由已知0q >，由题意得21111+123214a q a q a a q ⎧=⎪⎨+=⎪⎩，所以275180q q --=，解得2q=，12a =.因此数列{}n a 的通项公式为2n n a =.（2）由（1）知，22122111111()log log (21)(21)22121n a n b a a n n n n +-===-+--+，∴11111111(1)(1)2335212122121n nT n n n n =-+-++-=-=-+++.19．（1）X 所有可能的取值为0，1，2，3，4，5，6， ()11105525P X ==⨯=，()1111210525P X ==⨯⨯=， ()11121722101055100P X ==⨯+⨯⨯=，()121313221055105P X ==⨯⨯+⨯⨯=， ()2231114255101050P X ==⨯+⨯⨯=，()2365251025P X ==⨯⨯=，()33961010100P X ==⨯=， X ∴的分布列为X 0 1 2 3 4 5 6 P125125171001511506259100（2）选择延保方案一，所需费用1Y 元的分布列为：()111116960007500900010500120008580455025100E Y =⨯+⨯+⨯+⨯+⨯= (元)选择延保方案二，所需费用2Y 元的分布列为：2Y 77407740a+77402a+P671006259100()()()2676921774077407740277401002510050aE Y a a =⨯+⨯++⨯+=+(元) ()()122184050aE Y E Y ∴-=-， 当()()1221840050aE Y E Y -=->，即02000a <<时，选择方案二， 当()()1221840050aE Y E Y -=-=，即2000a =时，选择方案一，方案二均可， 当()()1221840050aE Y E Y -=-<，即2000a >时，选择方案一．20. （1）证明：因为AD AB ⊥，平面ABD ⊥平面ABC ，平面ABD 平面ABC AB =，AD ⊂平面ABD ，所以AD ⊥平面ABC ， 因为BC ⊂平面ABC ，所以AD BC ⊥．因为AB BC AC =，所以222AB BC AC +=，所以AB BC ⊥， 因为ADAB A =，所以BC ⊥平面ABD ．（2）解：设()04AD x x =<<，则4AB BC x ==-，四面体ABCD 的体积()()()2321114816326V f x x x x x x ==⨯-=-+()04x <<．()()()()2113161643466f x x x x x =-+=--'， 当403x <<时，()0f x '>，()V f x =单调递增； 当443x <<时，()0f x '<，()V f x =单调递减． 故当43AD x ==时，四面体ABCD 的体积取得最大值．以B 为坐标原点，建立空间直角坐标系B xyz -，则()0,0,0B ，80,,03A ⎛⎫ ⎪⎝⎭，8,0,03C ⎛⎫ ⎪⎝⎭，840,,33D ⎛⎫ ⎪⎝⎭，44,,033E ⎛⎫⎪⎝⎭．设平面BCD 的法向量为(),,x y z =n ，则00BC BD ⎧⎪⎨⎪⎩⋅=⋅=n n ，即80384033x y z ⎧⎪=+⎨=⎪⎪⎪⎩，令2z =-，得()0,1,2=-n ，同理可得平面BDE 的一个法向量为()1,1,2=-m ，则==． 由图可知，二面角C BD E --为锐角，故二面角C BD E --．21. （1）由题可知当点P 在椭圆O 的上顶点时，PAB S △最大，此时122PABS ab ab =⨯==△222122ab c a a a b c ⎧=⎪⎪=⇒=⎨⎪⎪-=⎩，b =1c =， ∴椭圆O 的标准方程为22143x y +=．（2）设过点()2,0B 与圆E 相切的直线方程为()2y k x =-，即20kx y k --=， ∵直线与圆E ：()2222x y r +-=相切，∴d r ==，即得()2224840r k k r -++-=．设两切线的斜率分别为1k ，()212k k k ≠，则121k k =，设()11,C x y ，()22,D x y ，由()()12222221112341616120143y k x k x k x k x y =-⎧⎪⇒+-+-=⎨+=⎪⎩， ∴211211612234k x k -=+，即211218634k x k -=+，∴11211234k y k -=+；同理：22212222186863443k k x k k --==++，212222112123443k k y k k --==++；∴()112221111222211112211121243348686414334CD k k y y k k k K x x k k k k k ----++===---+-++， ∴直线CD 的方程为()21112221111286343441k k k y x k k k ⎛⎫-+=- ⎪ ⎪+++⎝⎭． 整理得()()()()111222111714412141k k k y x x k k k =-=-+++，∴直线CD 恒过定点()14,0．22．（1）证明：设()()21111ln 14x f x a x x x ϕ⎡⎤⎛⎫=--+=+-⎢⎥ ⎪⎝⎭⎢⎥⎣⎦，定义域为()0,+∞，则()22111x x x x xϕ'-=-=． 当01x <<时，()0x ϕ'<；当1x >时，()0x ϕ'>， 故()x ϕ在()0,1内是减函数，在()1,+∞内是增函数， 所以1x =是()x ϕ的极小值点，也是()x ϕ的最小值点，所以()()()min10x x ϕϕϕ≥==，所以()21114f x a x ⎛⎫≥-+ ⎪⎝⎭．（2）解：函数()f x 的定义域为()0,+∞，()()()23233211111212222x x x x f x x x x x x '+---=--==， 当01x <<时，()0f x '<；当1x >时，()0f x '>， 所以()f x 在()0,1内是减函数，在()1,+∞内是增函数， 所以1x =是()f x 的极小值点，也是()f x 的最小值点， 即()()min 1f x f a ==， 若0a =，则()()()()221311132444x x f x g x x x x -+-=+-=-， 当01x <<时，()()f x g x >；当1x =时，()()f x g x =； 当1x >时，()()f x g x <． 所以()()(),01,1f x x h xg x x ⎧<<⎪=⎨≥⎪⎩，于是()h x 只有一个零点1x =．当0a >，则当01x <≤时，()()f x g x >，此时()()0h x f x a =≥>， 当1x >时，()0f x a >>，()0g x >，此时()0h x >， 所以()h x 没有零点．当0a <，则当01x <<时，根据（1）可知，()21114f x a x ⎛⎫≥-+ ⎪⎝⎭，江苏南通 8而01<，所以()211104f a >-+=， 又因为()()min 10f x f a ==<，所以()f x 在()0,1上有一个零点0x ， 从而一定存在()01,c x ∈，使得()()f c g c =， 即21130244a c c +-+=，所以2311424a c c-=+． 当x c >时，()()22211311112024224444c x c x g x f x a x x c cx cx x x c -+⎛⎫-=--+-=--++=-+> ⎪⎝⎭， 所以()()g x f x >，从而()()(),0,f x x ch x g x x c ⎧<≤⎪=⎨>⎪⎩，于是()h x 有两个零点0x 和1．故当0a <时，()h x 有两个零点．综上，当0a =时，()h x 有一个零点，当0a >时，()h x 没有零点，当0a <时，()h x 有两个零点．。